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Transition probabilities of Lévy-type processes: Parametrix construction
Franziska Kühn · 2017-02-03 · via math.PR updates on arXiv.org

We present an existence result for Lévy-type processes which requires only weak regularity assumptions on the symbol $q(x,ξ)$ with respect to the space variable $x$. Applications range from existence and uniqueness results for Lévy-driven SDEs with Hölder continuous coefficients to existence results for stable-like processes and Lévy-type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of Lévy and Lévy-type processes. The paper includes an extensive list of Lévy(-type) processes satisfying the assumptions of our results.

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